Convolution can describe the diffusion of information, for example, the diffusion that takes place if you put milk into your coffee and do not stir can be accurately modeled by a convolution operation (pixels diffuse towards contours in an image). In quantum mechanics, it describes the probability of a quantum particle being in a certain place when you measure the particle’s position (average probability for a pixel’s position is highest at contours). In probability theory, it describes cross-correlation, which is the degree of similarity for two sequences that overlap (similarity high if the pixels of a feature (e.g. nose) overlap in an image (e.g. face)). In statistics, it describes a weighted moving average over a normalized sequence of input (large weights for contours, small weights for everything else). Many other interpretations exist.